Years ago, when I got serious about black powder, I was where you are at O.P.
Several people with LOTS of experience told me to go .357. I didn't listen and spent a lot of time shooting 38/40 instead.
Finally, it just got to be too much work to keep a battery of guns fed with 38/40, so I started loading black powder in .357. I've never looked back. And, I wish I would have taken the advice I was given to begin with.
If you use .357 cases, you'll have no more problem with blow-back than with a WCF cartridge -- all things being equal with respect to chamber dimensions and so forth.
I've never gotten any rifle caliber to run an entire six-stage match without attention, regardless of caliber. But, the amount of attention is slight, really.
Go .357. Especially since it's what you got.
The one thing I would caution you about, however, is switching back and forth between black powder and smokeless loads. Find a bullet you like that is lubed with BP lubricant and use it exclusively for smokeless loads. Otherwise, it seems like it takes a match, or two, to get all the petroleum lube out of the gun so things don't gum up.